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Register a new userNo resonant tunneling in standard scalar quantum field theory
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We investigate the nature of resonant tunneling in Quantum Field Theory. Following the pioneering work of Banks, Bender and Wu, we describe quantum field theory in terms of infinite dimensional quantum mechanics and utilize the ``Most probable escape path (MPEP) as the class of paths which dominate the path integral in the classically forbidden region. Considering a 1+1 dimensional field theory example we show that there are five conditions that any associated bound state in the classically allowed region must satisfy if resonant tunnelling is to occur, and we then proceed to show that it is impossible to satisfy all five conditions simultaneously.
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The resonant tunneling phenomenon is well understood in quantum mechanics. We argue why a similar phenomenon must be present in quantum field theory. We then use the functional Schrodinger method to show how resonant tunneling through multiple barriers takes place in quantum field theory with a single scalar field. We also show how this phenomenon in scalar quantum field theory can lead to an exponential enhancement of the single-barrier tunneling rate. Our analysis is carried out in the thin-wall approximation.
A free massive scalar field in inhomogeneous random media is investigated. The coefficients of the Klein-Gordon equation are taken to be random functions of the spatial coordinates. The case of an annealed-like disordered medium, modeled by centered stationary and Gaussian processes, is analyzed. After performing the averages over the random functions, we obtain the two-point causal Greens function of the model up to one-loop. The disordered scalar quantum field theory becomes qualitatively similar to a $lambdaphi^{4}$ self-interacting theory with a frequency-dependent coupling.
We discuss the renormalisation of the initial value problem in quantum field theory using the two-particle irreducible (2PI) effective action formalism. The nonequilibrium dynamics is renormalised by counterterms determined in equilibrium. We emphasize the importance of the appropriate choice of initial conditions and go beyond the Gaussian initial density operator by defining self-consistent initial conditions. We study the corresponding time evolution and present a numerical example which supports the existence of a continuum limit for this type of initial conditions.
We study a free scalar field $phi$ in a fixed curved background spacetime subject to a higher derivative field equation of the form $F(Box)phi =0$, where $F$ is a polynomial of the form $F(Box)= prod_i (Box-m_i^2)$ and all masses $m_i$ are distinct and real. Using an auxiliary field method to simplify the calculations, we obtain expressions for the Belinfante-Rosenfeld symmetric energy-momentum tensor and compare it with the canonical energy-momentum tensor when the background is Minkowski spacetime. We also obtain the conserved symplectic current necessary for quantisation and briefly discuss the issue of negative energy versus negative norm and its relation to Reflection Positivity in Euclidean treatments. We study, without assuming spherical symmetry, the possible existence of finite energy static solutions of the scalar equations, in static or stationary background geometries. Subject to various assumptions on the potential, we establish non-existence results including a no-scalar-hair theorem for static black holes. We consider Pais-Uhlenbeck field theories in a cosmological de Sitter background, and show how the Hubble friction may eliminate what would otherwise be unstable behaviour when interactions are included.
We study the phase structure of a 4D complex scalar field theory with a potential V(Phi) = | Lambda^3 / Phi - Lambda Phi |^2 at zero and at finite temperature. The model is analyzed by mean field and Monte Carlo methods. At zero temperature the theory falls in the universality class of the 4D Ising model when varying Lambda. The situation is less clear-cut for variations w.r.t. Lambda at large temperatures and variations w.r.t. temperature at a given value of Lambda. We observe temperature independence of the mass of the first excitation.
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